FPP - Ch. 2 Exercises

Time Series Graphics

Dan Hong | dnaeye@gmail.com

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The following are my answers to the exercises in the excellent book Forecasting: Principles & Practice by Rob J Hyndman and George Athanasopoulos.

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1. Use the help function to explore what the series gold, woolyrnq and gas represent.

1a. Use autoplot() to plot several datasets from the fpp2 library.

library(fpp2)

Loading required package: ggplot2
Loading required package: forecast
Loading required package: fma
Loading required package: expsmooth

autoplot(gold)

autoplot(woolyrnq)

autoplot(gas)

1b. What is the frequency of each series?

frequency(gold)

[1] 1

frequency(woolyrnq)

[1] 4

frequency(gas)

[1] 12

1c. Use which.max() to spot outlier in gold series.

which.max(gold)

[1] 770

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2. Download the file tute1.csv from the book website, create a time series object, and plot its three time series.

2a. Read data from .CSV file to R dataframe.

tute1 <- read.csv("tute1.csv", header=TRUE)
View(tute1)

2b. Convert dataframe to time series.

mytimeseries <- ts(tute1[,-1], start=1981, frequency=4)

2c. Construct time series for each of the three series.

autoplot(mytimeseries, facets=TRUE)

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3. Download some monthly Australian retail data from the book website. These represent retail sales in various categories for different Australian states.

3a. Read data from Excel file using the readxl library.

retaildata <- readxl::read_excel("retail.xlsx", skip=1)

3b Select one of the time series in retaildata.

myts <- ts(retaildata[,"A3349335T"], frequency=12, start=c(1982,4))

3c. Plot the time series using various plotting functions.

autoplot(myts)

ggseasonplot(myts)

ggsubseriesplot(myts)

gglagplot(myts)

ggAcf(myts)

There is definitely an upward trend with clear seasonality peaks in March and December. Also, based on the ACF plot, the time series is very auto-correlated.

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4. Create time plots of several time series (shown below is just one example, goog).

#help(goog)
autoplot(goog) + ggtitle("Google") + xlab("Day") + ylab("Stock Price")

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5. Use ggseasonplot() and ggsubseriesplot() to explore seasonal patterns in several time series (shown below is just one example, writing).

ggseasonplot(writing)

ggsubseriesplot(writing)

August is clearly a down month. Every month is generally trending upward over the years. It’s very hard to detect unusual years using either of these charts, but based on ggsubseriesplot, across all months, there seems to have been a decline in a later year, maybe 1975.

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6. Use several graphics functions to explore features from several datasets (shown below is one example, usdeaths).

autoplot(usdeaths)

ggseasonplot(usdeaths)

ggsubseriesplot(usdeaths)

gglagplot(usdeaths)

ggAcf(usdeaths)

In terms of seasonality, there’s a consistent upward trend from February through July. From then, there’s a downward trend for the rest of the year, with slight bump ups in October and December. The ACF supports this observation and also indicates lack of any trend. There is no sign of cyclicity in any of the graphs.

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7. Use various plotting functions to explore the arrivals dataset and compare differences in arrivals to Australia from Japan, New Zealand, UK, and the US.

autoplot(arrivals[, 'Japan'])

ggseasonplot(arrivals[, 'Japan'])

ggsubseriesplot(arrivals[, 'Japan'])

autoplot(arrivals[, 'NZ'])

ggseasonplot(arrivals[, 'NZ'])

ggsubseriesplot(arrivals[, 'NZ'])

autoplot(arrivals[, 'UK'])

ggseasonplot(arrivals[, 'UK'])

ggsubseriesplot(arrivals[, 'UK'])

autoplot(arrivals[, 'US'])

ggseasonplot(arrivals[, 'US'])

ggsubseriesplot(arrivals[, 'US'])

Arrivals from Japan has definitely declined since the late 1990s and the UK to a lesser degree. Those from the US have remained about flat since 2000. Only New Zealand has seen an upward trend since the mid 2000s.

There are different seasonal patterns among the countries: * Japan: lower in Q2; about same other quarters * NZ: consistent incline from Q1 to Q3 and small decline in Q4 * UK: high in Q1 and Q4, low in Q2 and Q3 * US: similar to UK but less difference

NZ and UK patterns have been fairly consistent. Japan’s seasonal patterns evolved since the 1980s, with a marked increase in Q3. The US has had various patterns over the years, mostly in Q3.

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8. Match time plots with their ACF plots for four different time series.

• 1-B
• 2-A
• 3-D
• 4-C

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9. Plot the pigs time series and its ACF.

Use autoplot and ggAcf for pigs data (windowed from 1990 to end) to compare with white noise plots from Figures 2.17 and 2.18.

mypigs <- window(pigs, start=1990)
autoplot(mypigs)

ggAcf(mypigs)

Although mypigs is mostly white noise beginning with lag 4, there is some autocorrelation for lags 2 and 3 (usually ignore lag 1 autocorrelation) suggesting that it is not white noise. If one or more large spikes are outside these bounds, or if substantially more than 5% of spikes are outside these bounds, then the series is probably not white noise.

10. Use diff to difference the Dow Jones Index dataset dj to compute the daily changes in the index.

ddj <- diff(dj)
autoplot(ddj)

ggAcf(ddj)

The plot of differencing resembles white noise due to apparent mean reversion and lack of obvious trend. Almost all lags are within the dashed blue lines, indicating that the correlations are not significantly different from zero.